Tangent bundle geometry from dynamics: application to the Kepler problem

In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which are diffeomorphic with affine spaces. In particular, we consider the problem in connection with conformal vector fields of second order and apply the procedure to vector fields conformally related with the harmonic oscillator (f-oscillators) . We select one which covers the vector field describing the Kepler problem.Comment: 17 pages, 2 figure

Tensorial dynamics on the space of quantum states

A geometric description of the space of states of a finite-dimensional quantum system and of the Markovian evolution associated with the Kossakowski-Lindblad operator is presented. This geometric setting is based on two composition laws on the space of observables defined by a pair of contravariant tensor fields. The first one is a Poisson tensor field that encodes the commutator product and allows us to develop a Hamiltonian mechanics. The other tensor field is symmetric, encodes the Jordan product and provides the variances and covariances of measures associated with the observables. This tensorial formulation of quantum systems is able to describe, in a natural way, the Markovian dynamical evolution as a vector field on the space of states. Therefore, it is possible to consider dynamical effects on non-linear physical quantities, such as entropies, purity and concurrence. In particular, in this work the tensorial formulation is used to consider the dynamical evolution of the symmetric and skew-symmetric tensors and to read off the corresponding limits as giving rise to a contraction of the initial Jordan and Lie products.Comment: 31 pages, 2 figures. Minor correction

The Research on Moral and Civic Education in the Spanish Educational Theory – Evolution and current trends

With this paper the editors of the Journal of Social Science Education start a new kind of report which presents an overview of scholarly discourses on civic education and economic education in several European countries. The overall aim is to provide a first access to these discourses which are often rather difficult to reach. By publishing reports on these national scientific fields the editors of JSSE hope to facilitate the mutual perception of scholars and the development of a European discourse. The NECE database “Networking European Citizenship Education” which is available at http://www.nece.eu and at the German Federal Agency of Civic Education may help networking, too

Philosophy or education?. ¿Filosofía o educación?

Bajo Palabra, Revista de Filosofí

Expansion of the ligand knowledge base for chelating P,P-donor ligands (LKB-PP)

[Image: see text] We have expanded the ligand knowledge base for bidentate P,P- and P,N-donor ligands (LKB-PP, Organometallics2008, 27, 1372–1383) by 208 ligands and introduced an additional steric descriptor (nHe(8)). This expanded knowledge base now captures information on 334 bidentate ligands and has been processed with principal component analysis (PCA) of the descriptors to produce a detailed map of bidentate ligand space, which better captures ligand variation and has been used for the analysis of ligand properties

Transformed Institutions - Transformed Citizenship Education? Remarks on the current situation in Spain

Educational systems are placing great emphasis on the need to generate a sense of citizenship. In this article, we treat this question within the concrete framework of the recent history of Spain (from 1990 to current day). We make reference to three points: 1. The institutional framework of citizenship education; 2. The concepts of citizenship present in the school curriculum and the public debate; 3. The state of research into citizenship education. Based on our analysis of the situation in Spain, we draw several conclusions regarding international research projects on citizenship education

Aspects of asphaltene aggregation obtained from coarse-grained molecular modeling

We have performed a molecular-simulation-based study to explore some of the underlying mechanisms of asphaltene aggregation. The daunting complexity of the crude oil + asphaltene system precludes any type of meaningful molecular simulation unless some assumptions are made with respect to the key physical and chemical properties that must be explicitly described. In the present work, we focus on molecular simulations of a coarse-grained model of asphaltene molecules in pure solvents, which are based on the assumption that the general size asymmetry and asphaltene morphology play a key role in the aggregation process. We use simple single isotropic Lennard-Jones sites to represent paraffinic and aromatic C₆ segments, which are used as building blocks for the description of continental asphaltene models and solvent moieties. The energy and size parameters for the intermolecular models (ε and σ) for solute and solvent molecules are chosen to reproduce the experimental density of the liquid phase for different mixtures. An explicit pure solvent is considered, and the relationship between the aggregation mechanism and the solvent nature is investigated through direct simulation of the aggregation process. The results reproduce accurately expected trends observed for more-complex models as well as experiments, for example, strong aggregation of asphaltene molecules in <i>n-</i>heptane and high solubility in toluene. Different asphaltene models based on different geometries reveal that even at this level of simplification the topology of the molecules (number and position of aliphatic branches) does affect the way molecules aggregate

La revolución del amor como núcleo ético de la relación familiar

Este artículo ahonda en el núcleo constitutivo de la relación familiar a partir del diagnóstico de la revolución del amor. Para ello, recurre a algunas de las principales voces que se han ocupado de indagar las diferentes disposiciones amorosas que se dan en la relación de los amantes, del enamoramiento al amor-amistad basado en la conciencia comunal. Este recorrido lleva a concluir que la implicación más profunda de esa revolución del amor no es sólo de carácter sociológico, sino que la misma abre la puerta para entender el vínculo amoroso que fundamenta la vida familiar como una relación afectiva, pero también ética